Novelty and Collective Attention

The subject of collective attention is central to an information age where millions of people are inundated with daily messages. It is thus of interest to understand how attention to novel items propagates and eventually fades among large populations. We have analyzed the dynamics of collective attention among one million users of an interactive website -- \texttt{digg.com} -- devoted to thousands of novel news stories. The observations can be described by a dynamical model characterized by a single novelty factor. Our measurements indicate that novelty within groups decays with a stretched-exponential law, suggesting the existence of a natural time scale over which attention fades

Flow of emotional messages in artificial social networks

Models of message flows in an artificial group of users communicating via the Internet are introduced and investigated using numerical simulations. We assumed that messages possess an emotional character with a positive valence and that the willingness to send the next affective message to a given person increases with the number of messages received from this person. As a result, the weights of links between group members evolve over time. Memory effects are introduced, taking into account that the preferential selection of message receivers depends on the communication intensity during the recent period only. We also model the phenomenon of secondary social sharing when the reception of an emotional e-mail triggers the distribution of several emotional e-mails to other people.Comment: 10 pages, 7 figures, submitted to International Journal of Modern Physics

Economics-Based Optimization of Unstable Flows

As an example for the optimization of unstable flows, we present an economics-based method for deciding the optimal rates at which vehicles are allowed to enter a highway. It exploits the naturally occuring fluctuations of traffic flow and is flexible enough to adapt in real time to the transient flow characteristics of road traffic. Simulations based on realistic parameter values show that this strategy is feasible for naturally occurring traffic, and that even far from optimality, injection policies can improve traffic flow. Moreover, the same method can be applied to the optimization of flows of gases and granular media.Comment: Revised version of ``Optimizing Traffic Flow'' (cond-mat/9809397). For related work see http://www.parc.xerox.com/dynamics/ and http://www.theo2.physik.uni-stuttgart.de/helbing.htm

Properties of weighted complex networks

We study two kinds of weighted networks, weighted small-world (WSW) and weighted scale-free (WSF). The weight $w_{ij}$ of a link between nodes $i$ and $j$ in the network is defined as the product of endpoint node degrees; that is $w_{ij}=(k_{i}k_{j})^{\theta}$. In contrast to adding weights to links during networks being constructed, we only consider weights depending on the `` popularity\rq\rq of the nodes represented by their connectivity. It was found that the both weighted networks have broad distributions on characterization the link weight, vertex strength, and average shortest path length. Furthermore, as a survey of the model, the epidemic spreading process in both weighted networks was studied based on the standard \emph{susceptible-infected} (SI) model. The spreading velocity reaches a peak very quickly after the infection outbreaks and an exponential decay was found in the long time propagation.Comment: 14 pages, 5 figure

Evolution of reference networks with aging

We study the growth of a reference network with aging of sites defined in the following way. Each new site of the network is connected to some old site with probability proportional (i) to the connectivity of the old site as in the Barab\'{a}si-Albert's model and (ii) to $\tau^{-\alpha}$, where $\tau$ is the age of the old site. We consider $\alpha$ of any sign although reasonable values are $0 \leq \alpha \leq \infty$. We find both from simulation and analytically that the network shows scaling behavior only in the region $\alpha < 1$. When $\alpha$ increases from $-\infty$ to 0, the exponent $\gamma$ of the distribution of connectivities ($P(k) \propto k^{-\gamma}$ for large $k$) grows from 2 to the value for the network without aging, i.e. to 3 for the Barab\'{a}si-Albert's model. The following increase of $\alpha$ to 1 makes $\gamma$ to grow to $\infty$. For $\alpha>1$ the distribution $P(k)$ is exponentional, and the network has a chain structure.Comment: 4 pages revtex (twocolumn, psfig), 5 figure

Dendritic and axonal targeting patterns of a genetically-specified class of retinal ganglion cells that participate in image-forming circuits.

BackgroundThere are numerous functional types of retinal ganglion cells (RGCs), each participating in circuits that encode a specific aspect of the visual scene. This functional specificity is derived from distinct RGC morphologies and selective synapse formation with other retinal cell types; yet, how these properties are established during development remains unclear. Islet2 (Isl2) is a LIM-homeodomain transcription factor expressed in the developing retina, including approximately 40% of all RGCs, and has previously been implicated in the subtype specification of spinal motor neurons. Based on this, we hypothesized that Isl2+ RGCs represent a related subset that share a common function.ResultsWe morphologically and molecularly characterized Isl2+ RGCs using a transgenic mouse line that expresses GFP in the cell bodies, dendrites and axons of Isl2+ cells (Isl2-GFP). Isl2-GFP RGCs have distinct morphologies and dendritic stratification patterns within the inner plexiform layer and project to selective visual nuclei. Targeted filling of individual cells reveals that the majority of Isl2-GFP RGCs have dendrites that are monostratified in layer S3 of the IPL, suggesting they are not ON-OFF direction-selective ganglion cells. Molecular analysis shows that most alpha-RGCs, indicated by expression of SMI-32, are also Isl2-GFP RGCs. Isl2-GFP RGCs project to most retino-recipient nuclei during early development, but specifically innervate the dorsal lateral geniculate nucleus and superior colliculus (SC) at eye opening. Finally, we show that the segregation of Isl2+ and Isl2- RGC axons in the SC leads to the segregation of functional RGC types.ConclusionsTaken together, these data suggest that Isl2+ RGCs comprise a distinct class and support a role for Isl2 as an important component of a transcription factor code specifying functional visual circuits. Furthermore, this study describes a novel genetically-labeled mouse line that will be a valuable resource in future investigations of the molecular mechanisms of visual circuit formation

Intermittent exploration on a scale-free network

We study an intermittent random walk on a random network of scale-free degree distribution. The walk is a combination of simple random walks of duration $t_w$ and random long-range jumps. While the time the walker needs to cover all the nodes increases with $t_w$, the corresponding time for the edges displays a non monotonic behavior with a minimum for some nontrivial value of $t_w$. This is a heterogeneity-induced effect that is not observed in homogeneous small-world networks. The optimal $t_w$ increases with the degree of assortativity in the network. Depending on the nature of degree correlations and the elapsed time the walker finds an over/under-estimate of the degree distribution exponent.Comment: 12 pages, 3 figures, 1 table, published versio

Maximum flow and topological structure of complex networks

The problem of sending the maximum amount of flow $q$ between two arbitrary nodes $s$ and $t$ of complex networks along links with unit capacity is studied, which is equivalent to determining the number of link-disjoint paths between $s$ and $t$. The average of $q$ over all node pairs with smaller degree $k_{\rm min}$ is $_{k_{\rm min}} \simeq c k_{\rm min}$ for large $k_{\rm min}$ with $c$ a constant implying that the statistics of $q$ is related to the degree distribution of the network. The disjoint paths between hub nodes are found to be distributed among the links belonging to the same edge-biconnected component, and $q$ can be estimated by the number of pairs of edge-biconnected links incident to the start and terminal node. The relative size of the giant edge-biconnected component of a network approximates to the coefficient $c$. The applicability of our results to real world networks is tested for the Internet at the autonomous system level.Comment: 7 pages, 4 figure

Scaling Behaviour of Developing and Decaying Networks

We find that a wide class of developing and decaying networks has scaling properties similar to those that were recently observed by Barab\'{a}si and Albert in the particular case of growing networks. The networks considered here evolve according to the following rules: (i) Each instant a new site is added, the probability of its connection to old sites is proportional to their connectivities. (ii) In addition, (a) new links between some old sites appear with probability proportional to the product of their connectivities or (b) some links between old sites are removed with equal probability.Comment: 7 pages (revtex

Structure of Growing Networks: Exact Solution of the Barabasi--Albert's Model

We generalize the Barab\'{a}si--Albert's model of growing networks accounting for initial properties of sites and find exactly the distribution of connectivities of the network $P(q)$ and the averaged connectivity $\bar{q}(s,t)$ of a site $s$ in the instant $t$ (one site is added per unit of time). At long times $P(q) \sim q^{-\gamma}$ at $q \to \infty$ and $\bar{q}(s,t) \sim (s/t)^{-\beta}$ at $s/t \to 0$, where the exponent $\gamma$ varies from 2 to $\infty$ depending on the initial attractiveness of sites. We show that the relation $\beta(\gamma-1)=1$ between the exponents is universal.Comment: 4 pages revtex (twocolumn, psfig), 1 figur